Ditkin sets for some functional spaces and applications to grand Lebesgue spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916492940935168 |
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| author | Gürkanlı, A. Turan |
| author_facet | Gürkanlı, A. Turan |
| contents | Let $G$ be a locally compact Abelian group with dual group $\widehat G $ and Haar measures $dμ$ and $\hat dμ$ respectively. In this work we have proved that if $X$ is an essential Banach ideal in Beurling algebra $ L^1_ω(G),$ then a closed subset $E\subset \widehat G$ is a Ditkin set for $X$ if and only if $E$ is a Ditkin set for $ L^1_ω(G).$ Next, as an application we have investigated the Ditkin sets for grand Lebesgue space $L^{p),θ}(G)$ and Ditkin sets for $[L^p(G)]_{L^{p),θ}}$, where $[L^p(G)]_{L^{p),θ}}$ is the closure of the set $C_c(G)$ in $L^{p),θ}(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ditkin sets for some functional spaces and applications to grand Lebesgue spaces Gürkanlı, A. Turan Functional Analysis Let $G$ be a locally compact Abelian group with dual group $\widehat G $ and Haar measures $dμ$ and $\hat dμ$ respectively. In this work we have proved that if $X$ is an essential Banach ideal in Beurling algebra $ L^1_ω(G),$ then a closed subset $E\subset \widehat G$ is a Ditkin set for $X$ if and only if $E$ is a Ditkin set for $ L^1_ω(G).$ Next, as an application we have investigated the Ditkin sets for grand Lebesgue space $L^{p),θ}(G)$ and Ditkin sets for $[L^p(G)]_{L^{p),θ}}$, where $[L^p(G)]_{L^{p),θ}}$ is the closure of the set $C_c(G)$ in $L^{p),θ}(G)$. |
| title | Ditkin sets for some functional spaces and applications to grand Lebesgue spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2411.05539 |